WHITE = 1
BLACK = 2
UNKNOWN = WHITE|BLACK

def solve_line(hint, line):
    line = line + [WHITE] # make our life easier
    n = len(line)
    m = len(hint)

    result = [0]*n
    memo = {} # memoization table
    
    def f(i,j):
        """
        Try to see whether line[:i+1] can accomodate hint[:j+1]
        such that line[i] is white.
        """
        if i == -1:
            return j == -1
        if line[i] == BLACK: # must end in WHITE
            return False
        if (i,j) in memo:
            return memo[i,j]

        # can we just add one WHITE?
        opt1 = f(i-1, j)
        # can we fit the last BLACK hint in the end of line[:i] and the following WHITE at line[i-hint[j]-1]?
        opt2 = j>=0 and i>=hint[j] \
               and WHITE not in line[i-hint[j]:i] \
               and f(i-1-hint[j], j-1)

        if opt1:
            result[i] |= WHITE
        if opt2:
            result[i] |= WHITE
            for k in range(i-hint[j],i):
                result[k] |= BLACK
        memo[i,j] = answer = opt1 or opt2
        return answer

    assert f(n-1,m-1)
    return result[:-1] # drop the surplus WHITE